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International Conference on Principles and Practice of Constraint Programming

CP 2017: Principles and Practice of Constraint Programming pp 114–128Cite as

Arc Consistency via Linear Programming

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10416))

Abstract

A typical technique in integer programming for filtering variables is known as variable fixing. The optimal dual solution of the linear relaxation can be used to detect some of the 0/1 variables that must be fixed to either 0 or 1 in any solution improving the best known, but this filtering is incomplete. A complete technique is proposed in this paper for satisfaction problems with an ideal integer programming formulation. We show, in this case, that the 0/1 variables taking the same value in all solutions can be identified by solving a single linear program with twice the number of the original variables. In other words, a complete variable fixing of the 0/1 variables can be performed for a small overhead. As a result, this technique can be used to design generic arc consistency algorithms. We believe it is particularly useful to quickly prototype arc consistency algorithms for numerous polynomial constraints and demonstrate it for the family of Sequence global constraints.

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Authors and Affiliations

  1. CNRS, Grenoble INP G-SCOP, University Grenoble Alpes, 38000, Grenoble, France

    Grigori German, Olivier Briant, Hadrien Cambazard & Vincent Jost

Authors
  1. Grigori German
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  2. Olivier Briant
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  3. Hadrien Cambazard
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  4. Vincent Jost
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Corresponding author

Correspondence to Grigori German .

Editor information

Editors and Affiliations

  1. University of Toronto, Toronto, Ontario, Canada

    J. Christopher Beck

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German, G., Briant, O., Cambazard, H., Jost, V. (2017). Arc Consistency via Linear Programming. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_8

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  • DOI: https://doi.org/10.1007/978-3-319-66158-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66157-5

  • Online ISBN: 978-3-319-66158-2

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